This back reasoning is to get the missing premises according to partial
premises and the conclusion. The Syllogism is invented by Aristotle 300
B.C. The traditional expression is as follow:
((A -> B) & (B -> C)) -> (A -> C)
& is logic and, -> is implication. Now we are going to remove (B -> C)
and using X to replace it. The following formula is appeared
((A -> B) & X) -> (A -> C)
This is one form of the back reasoning. The unknown variable X could be
solved. When X = ((A -> C) <-> B), the new law is
((A -> B) & ((NEW -> (B & A)) -> C)) -> (A -> C)
This law can be read as (A -> C) could be reasoned from the conditions
(A -> B) and ((NEW -> (B & A)) -> C)